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Where did the area of a rhombus come from?
If you multiply the lengths of the two diagonals, and divide by 2, you get the area of a rhombus. How does this work: Call the diagonals A & B for clarity. Diagonal A will split the rhombus into 2 congruent triangles. Looking at one of these triangles, its base is the diagonal A, and its height is 1/2 of diagonal B. So the area of one of the triangles is (1/2)*base*height = (1/2)*A*(B/2) = A*B/4. The other triangle has the same area, so the two areas together make up the whole rhombus = 2*(A*B/4) = A*B/2.
How is finding the area of a rhombus similar to finding the area of a kite?
Because in both cases their diagonals cross at right angles So their areas are: 0.5*product of diagonals
What is the Practical application for finding the number of diagonals in a regular polygon?
The diagonals (drawn from a point) help in dividing the regular polygon into smaller triangles. The sum of the areas of these smaller triangles help in determining the total area of the polygon.
How do you find the area of a polygon using its vertices?
Select any one of the vertices and draw all the diagonals from that vertex. This will divide the polygon (with n sides) into n-2 triangles. Use the coordinates of the vertices of each triangle to calculate its area, and then add the areas of these triangles together.
How can you find the area of a polygon that is not one for which you know an area formula?
Divide the polygon into triangles. Calculate the areas of the triangles and then sum these.
Where did the area of a rhombus come from?
If you multiply the lengths of the two diagonals, and divide by 2, you get the area of a rhombus. How does this work: Call the diagonals A & B for clarity. Diagonal A will split the rhombus into 2 congruent triangles. Looking at one of these triangles, its base is the diagonal A, and its height is 1/2 of diagonal B. So the area of one of the triangles is (1/2)*base*height = (1/2)*A*(B/2) = A*B/4. The other triangle has the same area, so the two areas together make up the whole rhombus = 2*(A*B/4) = A*B/2.
How is finding the area of a rhombus similar to finding the area of a kite?
Because in both cases their diagonals cross at right angles So their areas are: 0.5*product of diagonals
What is the Practical application for finding the number of diagonals in a regular polygon?
The diagonals (drawn from a point) help in dividing the regular polygon into smaller triangles. The sum of the areas of these smaller triangles help in determining the total area of the polygon.
Show that the diagonals of parallelogram divide it into four triangles of equal area?
We know that diagonals of parallelogram bisect each other. Therefore, O is the mid-point of AC and BD. BO is the median in ΔABC. Therefore, it will divide it into two triangles of equal areas. Area (ΔAOB) = Area (ΔBOC) ... (1) In ΔBCD, CO is the median. Area (ΔBOC) = Area (ΔCOD) ... (2) Similarly, Area (ΔCOD) = Area (ΔAOD) ... (3) From equations (1), (2), and (3), we obtain Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD) Therefore, it is evident that the diagonals of a parallelogram divide it into four triangles of equal area.
How do you find the area of a polygon using its vertices?
Select any one of the vertices and draw all the diagonals from that vertex. This will divide the polygon (with n sides) into n-2 triangles. Use the coordinates of the vertices of each triangle to calculate its area, and then add the areas of these triangles together.
How do you get the square inches of a polygon?
In general, you divide up the polygon into triangles, calculate the areas of the triangles and then sum these.
How can you find the area of a polygon that is not one for which you know an area formula?
Divide the polygon into triangles. Calculate the areas of the triangles and then sum these.
How do you find area of a pentegon?
The only general way is to divide the pentagon into three triangles, calculate the areas of the triangles and add them together.
How do their areas triangles compare?
I'll be happy to help you, but in order for me to compare the areas of those triangles, you have to tell me the areas of those triangles.
How do you find the area of an icosahedron?
You would need to divide it into triangles, find the area of each triangle and sum these areas together.
What is the formula of getting the area of a heptagon?
There is no simple formula. You need to divide it into triangles, calculate the areas of each one and sum the results.
How do you find the area of an uneven shape?
One method is to divide it into regular shapes - rectangles, triangles, etc. - and measure the areas of those shapes.
